{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5CM3PTZWXXL4ZCSKONRMN3PJ5L","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6dd7952f01e21ca83737e412306318aa67a0687127c2fb125f8248e80b5d1375","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-07-19T10:03:24Z","title_canon_sha256":"65ee742bf9bd159a2a2a5ea18703d4dc9c21e65e82a88fa655effa471e9f6627"},"schema_version":"1.0","source":{"id":"1707.06001","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.06001","created_at":"2026-05-18T00:10:24Z"},{"alias_kind":"arxiv_version","alias_value":"1707.06001v1","created_at":"2026-05-18T00:10:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06001","created_at":"2026-05-18T00:10:24Z"},{"alias_kind":"pith_short_12","alias_value":"5CM3PTZWXXL4","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5CM3PTZWXXL4ZCSK","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5CM3PTZW","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:fab95ea150bee20fd698a42461ce173f4afc449af6772100d4c827f04404dd5d","target":"graph","created_at":"2026-05-18T00:10:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We present the fractional perimeter as a set-function interpolation between the Lebesgue measure and the perimeter in the sense of De Giorgi. Our motivation comes from a new fractional Boxing inequality that relates the fractional perimeter and the Hausdorff content and implies several known inequalities involving the Gagliardo seminorm of the Sobolev spaces $W^{\\alpha, 1}$ of order $0 < \\alpha < 1$.","authors_text":"Augusto C. Ponce, Daniel Spector","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-07-19T10:03:24Z","title":"A note on the fractional perimeter and interpolation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06001","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7575947995c83c6b58c3fd7344b1b8bd72e253854bdfaea5604cb5ece4abfa92","target":"record","created_at":"2026-05-18T00:10:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6dd7952f01e21ca83737e412306318aa67a0687127c2fb125f8248e80b5d1375","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-07-19T10:03:24Z","title_canon_sha256":"65ee742bf9bd159a2a2a5ea18703d4dc9c21e65e82a88fa655effa471e9f6627"},"schema_version":"1.0","source":{"id":"1707.06001","kind":"arxiv","version":1}},"canonical_sha256":"e899b7cf36bdd7cc8a4a7362c6ede9eac2ab3ac128c3c4d71aa8f3607873c140","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e899b7cf36bdd7cc8a4a7362c6ede9eac2ab3ac128c3c4d71aa8f3607873c140","first_computed_at":"2026-05-18T00:10:24.412363Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:24.412363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s/hl3ELAd3xKAEhUvwK+q1aBRKREfbsmo8oUFjglURh34FZlC1HrIMQIEOEYOnE9b5sNMTKufhQ/JmRcN0C4Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:24.413026Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.06001","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7575947995c83c6b58c3fd7344b1b8bd72e253854bdfaea5604cb5ece4abfa92","sha256:fab95ea150bee20fd698a42461ce173f4afc449af6772100d4c827f04404dd5d"],"state_sha256":"6d400c7a5e68d3173b4424c56fb3a4a9c29d834dbf753e3ac478c555ed9d1508"}